Mathematical Issue with Stock to Flow

So regardless of other issues with the infamous S2F price prediction model, one aspect of it in particular has been bugging me for a while and I finally decided to sit down and express it here.

PlanB’s last article on the S2F model used stock-to-flow and market cap values from multiple assets to come up with a price prediction formula using logistic regression. The following is what he got:

Market Cap = exp(12.7598) * S2F ^ 4.1167

To his credit, this model does seem to fit quite well with Bitcoin price history as well as the S2F and market caps of gold and silver.

Despite the accuracy of the model on real world prices, the issue that has been bugging me is that if Bitcoin in reserve is ever lost (due to lost keys or intentional burning) this formula predicts a lower Bitcoin price. For example, assuming 19M Bitcoin and a block reward of 6.25 (382,500 BTC per year), that equates to an S2F of 49.67 and a market cap of $3.3T and a per BTC price of $175k. If a private key to a wallet containing 1 million BTC were lost, this would take S2F to 47, the market cap to $2.7T and a per BTC price of $149k.

This does not make intuitive sense. In fact, people regularly say that lost keys are “a donation to the network” as it is widely understood that lost Bitcoin should only ever increase the value of all remaining Bitcoin.

This S2F model, while reflecting the data accurately, does not mechanically make intuitive sense. There must be something missing and there is likely a more theoretically sound model to be constructed.

I suspect that S2F itself does not have a direct causal relationship on the price. Rather, what is probably going on is that the flow element (and thus S2F) is a consequence of how easy it is to increase the supply of an asset given the current price, or rather the supply elasticity. In my opinion, it is the supply elasticity and the aggregate demand (which is itself likely a function of total adoption and supply elasticity), and that S2F is a variable that tends to be a proxy of these mechanics given a long enough time period for total supply vs. supply elasticity to converge and for demand/adoption to reflect supply elasticity.

Of course, these are just some spitball thoughts trying to wrap my head around the intuitive discrepancies of the S2F model.